# ALEX Lesson Plan

## Triangle Congruence with Rigid Motions

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This lesson provided by:
 Author: Morgan Boyd Organization: Retirement
General Lesson Information
 Lesson Plan ID: 35593 Title: Triangle Congruence with Rigid Motions Overview/Annotation: This lesson will provide instruction on proving triangles to be congruent using rigid motions. Using the concept of transformations, the students will be able to manipulate the triangle on the coordinate plane. When using the coordinate plane to test congruence, the triangle or other object will slide, rotate, or flip to map onto the other object. Sometimes, the student will use a combination of the transformations. This lesson results from the ALEX Resource Gap Project.
Associated Standards and Objectives
Content Standard(s):
 Mathematics MA2019 (2019) Grade: 9-12 Geometry with Data Analysis 25. Verify criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another. a. Verify that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. b. Verify that two triangles are congruent if (but not only if) the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), side-side-side (SSS), and angle-angle-side (AAS). Example: Given two triangles with two pairs of congruent corresponding sides and a pair of congruent included angles, show that there must be a sequence of rigid motions will map one onto the other. Alabama Alternate Achievement Standards AAS Standard: M.G.AAS.10.24 When given two congruent triangles that have been transformed (limit to a translation), determine the congruent parts. (Ex: Determine which leg on Triangle A is congruent to which leg on Triangle B.)

Local/National Standards:

Primary Learning Objective(s):

The student will be able to explain the techniques of transformations to prove triangles congruent.

The student will be able to prove triangles congruent by SSS, ASA, SAS or AAS.

The student will be able to explain the differences of each type of transformation.

The student will be able to combine transformations to prove triangles are congruent.

Preparation Information
 Total Duration: 31 to 60 Minutes Materials and Resources: PowerPoint Presentation that will explain step by step during the class: "Congruent Triangles" (see attached presentation)PencilsNotebook paperScissors (if necessary)Graph Paper (see attached file, make copies as needed)Exit Slip Transformations with Answers (see attached file make copies for all students)"SSS, SAS, ASA, and AAS congruences combined" and "All transformations combined" from Kuta Software (make copies for each student)https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangleshttp://www.watchknowlearn.org/Video.aspx?VideoID=18777 Technology Resources Needed: Desktop computer with PowerPoint softwareProjector and/or interactive whiteboard for displaying videos and PowerPointiPad, Chromebook, or MacBook for students to revisit websites used in classWebsites:Khan Academy "Congruent Triangles"-https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-trianglesWatch Know Learn- http://www.watchknowlearn.org/Video.aspx?VideoID=18777Kuta Software (worksheet generator)- https://www.kutasoftware.com/freeige.html. The triangle congruence and transformation worksheets are on this page. The worksheets will open in another tab. Background/Preparation: Teacher:The teacher will preview the PowerPoint presentation. The teacher needs to visit the website Kuta Software. Kuta Software has free worksheets that can be printed and copied. The teacher needs to preview the videos to determine when to stop and ask questions.Student:The student needs to be able to graph points on the coordinate plane. The student needs to be familiar with transformations and how triangles can be congruent. The three transformations are translation, reflection, and rotation. Three common ways to prove triangle congruence are as follows: Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle.
Procedures/Activities: